Mathematicians and geochemists have long realized that compositional data intrinsically exhibit a structure prone to spurious and induced correlations. This paper demonstrates, using the Na–Cl–Br system, that these mathematical problems are exacerbated in the study of sedimentary basin brines by such processes as the evaporation or dissolution of salts owing to their high salinities. Using two published datasets of Na–Cl–Br data for fluids from the Appalachian Basin, it is shown that log concentration and Na/Br versus Cl/Br methods for displaying solute chemistry may lead to misinterpretation of mixing trends between meteoric waters (for example shallow drinking water aquifers) and basinal brines, partially due to spurious mathematical relationships. An alternative approach, based on the isometric log-ratio transformation of molar concentration data, is developed and presented as an alternative method, free from potential numerical problems of the traditional methods. The utility, intuitiveness, and potential for mathematical problems of the three methods are compared and contrasted. Because the Na–Cl–Br system is a useful tool for sourcing solutes and investigating the evolution of basinal brines, results from this research may impact such critical topics as evaluating sources of brine contamination in the environment (possibly related to oil and gas production), evaluating the behavior of fluids in the reservoir during hydraulic fracturing, and tracking movement of fluids as a result of geologic CO2 sequestration.
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This research was funded by the U.S. Geological Survey Energy Resources Program. The authors would also like to acknowledge Lin Ma (University of Texas at El Paso), Jennifer McIntosh (University of Arizona, U.S. Geological Survey), Ricardo Olea (U.S. Geological Survey), Josep Antoni Martín Fernández (Universitat de Girona), and two anonymous journal reviewers for providing critical comments and corrections to this paper.
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Engle, M.A., Rowan, E.L. Interpretation of Na–Cl–Br Systematics in Sedimentary Basin Brines: Comparison of Concentration, Element Ratio, and Isometric Log-ratio Approaches. Math Geosci 45, 87–101 (2013). https://doi.org/10.1007/s11004-012-9436-z
- Isometric log-ratio
- Compositional data analysis
- Appalachian Basin
- Produced Water